A neutron detector has been constructed and calibrated for the accurate measurement of total neutron production cross sections. The detector consists of a polyethylene sphere of 60 cm diameter in which eight /sup 10/BF/sub 3/ counters have been installed radially. The relative efficiency of this detector has been determined for average neutron energies from 30 keV to 1.5 MeV by counting neutrons from /sup 7/Li(p, n)/sup 7/Be. By adjusting the radial positions of the BF/sub 3/ counters in the polyethylene sphere the efficiency for neutron detection was made nearly constant for this energy range. Measurement of absolute efficiency for the same neutron energy range has been done by counting the neutrons from /sup 51/V(p, n)/sup 51/Cr and /sup 57/Fe(p, n)/sup 57/Co reactions and determining the absolute number of residual nuclei produced during the measurement of neutron yield. Details of absolute efficiency measurements and the use of the detector for determination of neutron production cross sections are given.